DESIGNING POWER SYSTEM STABILIZER FOR MULTIMACHINE POWER SYSTEM
55
Jurnal Teknologi, 35(D) Dis. 2001: 55–64
© Universiti Teknologi Malaysia
DESIGNING POWER SYSTEM STABILIZER FOR
MULTIMACHINE POWER SYSTEM USING NEURO-FUZZY
ALGORITHM
M. F. OTHMAN1, M. MAHFOUF2 & D. A. LINKENS3
Abstract. This paper describes a design procedure for a fuzzy logic based power system stabilizer (FLPSS) and adaptive neuro-fuzzy inference system (ANFIS) and investigates their robustness
for a multi-machine power system. Speed deviation of a machine and its derivative are chosen as
the input signals to the FLPSS. A four-machine and a two-area power system is used as the case
study. Computer simulations for the test system subjected to transient disturbances i.e. a three
phase fault, were carried out and the results showed that the proposed controller is able to prove
its effectiveness and improve the system damping when compared to a conventional lead-lag
based power system stabilizer controller.
1.0
INTRODUCTION
Low frequency oscillations occur in power systems due to disturbances. If no
adequate damping is available, such oscillations can increase and cause system
separation. Power system stabilizers (PSS) are installed in power systems generators
to enhance damping [6] and provide supplementary feedback stabilizing signals
which extend the power stability limits.
Under the conventional PSSs, the proposed eigenvalue assignment technique is
iterative and leads to heavy computations, which give rise to time-consuming computer codes [1]. Furthermore, the initialization step is crucial and affects the final
dynamic response of the controlled system. From a given set of eigenvalues,
different designs can be obtained by simply altering the parameters involved in the
initialisation step.
Mathematical programming techniques have been applied to assist in the final
criteria of these conventional PSSs [4], however, they disregard conservativeness
and cause the number of constraints to increase considerably. The optimization
process requires the computations of sensitivity factors and eigen-factors at each
iteration. This results in heavy computational tasks and slow convergence. The search
process will somehow be trapped in local minima and the solution obtained will not
be optimal.
1, 2 & 3
Untitled-58
Department of Automatic Control and System Engineering, The University of Sheffield
othman@acse.sheff.ac.uk, m.mahfouf@sheffield.ac.uk, d.linkens@sheffield.ac.uk
55
02/16/2007, 18:06
56
M. F. OTHMAN, M. MAHFOUF & D. A. LINKENS
As far as modern control theory is concerned, several approaches have been
proposed to improve the PSS design problem; these include optimal control, adaptive control, variable structure control and intelligent control [2, 4]. The present
paper introduces a power stabilizer based on fuzzy logic and ANFIS design controllers. The influence of the proposed FLPSS design on the dynamic characteristics of
the controlled system is investigated. Simulation results to illustrate the effectiveness
of the proposed controller are presented. These results have been obtained from a
simulation study on a four-machine power network. In this study, the system has
been subjected to a severe type of disturbance, i.e. a sudden three-phase short circuit fault at the end of one of the system busbars. This test demonstrates the enhancement of the transient stability of the system.
In this Fuzzy logic based design, a rule was extracted from a conventional controller to give an initial solution. A speed deviation and its derivative are used as an
input to the PSS controller. The Neuro-fuzzy technique is used as a second design
method. Training data are taken from the output of a conventional controller and
are fed to ANFIS for training. The proposed design approaches are applied to a 4
machine two-area power system. Different size of an input/output membership function and defuzzification methods are used to assess the effectiveness of the proposed
controller in terms of damping out the electromechanical modes of oscillation.
2.0
FUZZY LOGIC POWER SYSTEM STABILIZER
Τhe initial step in designing the FLPSS is the determination of the state variables
which represent the performance of the system. The input signals to the FLPSS are
to be chosen from these variables. The input values are normalized and converted
into fuzzy variables. Rules are executed to produce a consequent fuzzy region for
each variable. The expected value for each variable is found by defuzzifying the
fuzzy regions. The Speed Deviation (ω) of the synchronous machine and its derivative (w) are chosen as inputs to the FLPSS and the output is the stabilizing signal
Upss. This signal is fed as one of the inputs to the excitation system.
The proposed controller also uses 7 linguistic variables such as: Positive Big (PB),
Positive Medium (PM), Positive Small (PS), Zero (ZR), Negative Small (NS), Negative Medium (NM) and Negative Big (NB)
The membership functions are chosen to be trapezoidal if the input signal is “PB”
or “NB” and triangular or gaussian for the others. The defuzzification of the fuzzy
variables into crisp outputs is tested by using the center of gravity (COG) and the
Mean of Maxima (MOM) methods.
2.1
Training the Controller
Physical domains can be calculated from the generated data for simulation by the
conventional controller attached initially at both generators.
Untitled-58
56
02/16/2007, 18:06
DESIGNING POWER SYSTEM STABILIZER FOR MULTIMACHINE POWER SYSTEM
57
For the rule-base, the relationship between the fuzzy controller inputs and its
output can be extracted from the following algorithm:
1. simulate the conventional controller.
2. Save each sample value of (∆ω , change in ∆ω, and Upss)
3. At each sample time t:
∆ω ∈ the class with max membership among (NB,NM,NS,ZR,PS,PM,PB)
so at sample time ∆ω is ω_1
... (a)
change in ∆ω ∈ the class with max membership among (NB,NM,NS,
ZR,PS,PM,PB )
so at sample time t , ∆ω is ω_1
... (b)
This will form the contents of the rule-antecedent (If-part of a rule)
Upss ∈ the class with max membership among (NB,NM,NS,ZR,PS,PM,PB)
so at sample time t , Upss is? u_1
... (c)
The contents of the rule-consequent (then-part of the rule)
And a total rule can be formed as:
From (a), (b) and (c): the rule “If ∆ω is ω_1 and change in ∆ω is dω_1 then
Upss is u_1”
After generating the rules, the tuning procedures are carried out manually by
observation of the control surface relating to the controller. A sample of these rules
is shown in Table 1.
Table 1 Rule Extracted from the conventional controller
Speed
Dev
2.2
Acceleration
NB
NM
NS
ZR
PS
PM
PB
NB
NB
NB
NB
NB
NM
NS
ZR
NM
NB
NB
NM
NM
NS
ZR
PS
NS
NB
NM
NS
NS
ZR
PS
PM
ZP
NM
NM
NS
ZR
ZR
PM
PM
PS
NM
NS
ZR
ZR
PS
PM
PB
PM
NS
ZR
PS
PM
PM
PM
PB
PB
ZR
ZR
PM
PB
PB
PB
PB
ANFIS Controller
In MATLAB, the ANFIS editor graphics user interface is available in Fuzzy Logic
Toolbox [7]. Using a given input/output data set, the toolbox constructs a fuzzy
Untitled-58
57
02/16/2007, 18:06
58
M. F. OTHMAN, M. MAHFOUF & D. A. LINKENS
inference system (FIS) whose membershi p function parameters are adjusted using
either a backpropagation algorithm alone, or in a combination with a least squares
type of method. This allows the fuzzy systems to learn from the data they are
modeling.
For the backpropagation-based NF approach, it includes the Sugeno’s model
with the following format:
Ri : if speed deviation error is w and the acceleration is w, then Upss
fx = piw + qi w + ri
(1)
where i = (1, n * m) refers to the rule number,
j = (1, n) refers to the Speed Deviation Error terms in the xe fuzzy set,
n, m refers to the number of terms generated,
k = (1, m) refers to the acceleration terms in the fuzzy set,
n, m pi, qiri is the ith consequent (PSS output) parameters.
In the ANFIS Editor, the fuzzy inference is generated using two partition
methods; grid partitioning and subtractive clustering. For grid partitioning, it uses
the Fuzzy C-means clustering (FCM) data clustering technique. FCM is a data
clustering algorithm in which each data point belongs to a cluster with a degree
specified by a membershi p grade.
After generating the fuzzy inference, the generated information describing the
model’s structure and parameters of both the input and output variables are used in
the ANFIS training phase. This information will be fine-tuned by applying the
hybrid learning or the backpropagation schemes. The generated model is of a
first-order Sugeno’s form and the generated rules in the form described in equation
(1). After this stage, the MFs will be adjusted to optimise the controller action (see
Figure 1).
The input signals to the ANFIS controller for the PSS are ω and w. The ANFIS
controller parameters generated by the ANFIS Editor, based on two inputs and 331
training data points, are as follows:
(1)
(2)
(3)
(4)
(5)
Untitled-58
Number of nodes
Number of linear parameters
Number of nonlinear parameters
Total number of parameters
Number of fuzzy rules
58
: 75
: 75
: 20
: 95
: 25
02/16/2007, 18:06
DESIGNING POWER SYSTEM STABILIZER FOR MULTIMACHINE POWER SYSTEM
59
Gathering data plan
Identity the process inputs
& output variables.
Determine the number of data
samples.
Simulation operation
Load the fuzzy inference system
& run.
ANFIS training
Load the data to the
ANFIS Editor.
Data validation
Generate FIS.
N
OK
Y
Stop
Figure 1 Anfis Design Procedure for PSS
3.0
SIMULATION RESULTS
The single-line diagram of the two-area, 4-machine test system, as shown in Figure 2,
is used to examine both local and inter-area oscillations control problems. This
system is created especially for the analysis and study of the inter-area oscillation
problem [6].
10
20
3
101
13
120
110
GEN1
GEN11
102
967 MW 1767 MW
GEN2
GEN12
Figure 2 4 Machine-Two Area System
Untitled-58
59
02/16/2007, 18:07
60
M. F. OTHMAN, M. MAHFOUF & D. A. LINKENS
As shown in the above single-line diagram there are four generators, GEN1 and
GEN2 for area #1, GEN11 and GEN12 for area #2, and four 20/230 kV step-up
transformers. There are two loads in the system at buses 3 and 13. This system
exhibits three electromechanical modes of oscillations where one inter-area mode of
the generating units in one area oscillates against those in the other area. The frequency of this mode varies from 0.35 to 0.75 Hz depending on the operating conditions. Two local modes represent oscillations between the generating units within
each area. The frequency of the local modes is around 1.3 Hz and the loads are
modeled as constant impedances. One set of FLPSS controllers is used for generator
number one and one conventional-PSS for generator number two.
In order to test the robustness of the proposed design procedure of FLPSS, an
experiment was carried-out for a three-phase to ground fault at the middle of one
transmission line between busses 3 and 13, which is cleared after 0.05 seconds by
tri pping the fault-line. A comparison between the results of a lead-lag and fuzzy
controllers in the face of different disturbances is presented. The results of the simulations can be divided into three parts depending on which controller is used:
(a) For the Conventional Controller.
(b) For the Fuzzy Logic Controller.
(c) For the ANFIS Controller.
For the conventional controller, a double lead-lag compensator taken from Power
System Toolbox (PST 1997) is used.
For designing the FLPSS, a Mamdani Type FL is used for both inputs and output
with 3 Membership Functions(MF’s), 5 MF’s and 7MF’s and COG and MOM
defuzzification methods. The results show that the oscillations are damped more
effectively when the FLPSS and the ANFIS are used. From all the results shown in
Figure 3 Membershi p Function Control Surface
Untitled-58
60
02/16/2007, 18:07
DESIGNING POWER SYSTEM STABILIZER FOR MULTIMACHINE POWER SYSTEM
61
Figure 3 to Figure 9, it can be seen that the mixed-Gaussian/ Triangular MF gives the
best results compared with the others. Here best means reaching the steady state
condition in the shortest time and with a minimum deviation. By using the MOM
defuzzification method, (see in Figure 6), the controller settles at zero as the rules
move abruptly from each cell to cell. This is expected since the MOM is more suited
for decision making problems.
The control surface for the Mixed-MF is shown in Figure 3. There is a small flat
region in the origin to guarantee equilibrium. The small flat region in the origin is
followed by sharp slopes in all direction to reflect non-linearity and to provide a
quick response from the controller to even small deviations in the speed or acceleration of the rotor.
4.0 CONCLUSION
The work in this research involves a fuzzy logic and ANFIS controller, which is built
based on the data generated by the conventional controller. The generation of fuzzy
rule-based and input-output domain ranges has been investigated. It has been found
that the FLPSS provides more robust control against severes disturbances with quicker
settling-times when compared with a conventional lead-lag stabilizer.
Speed Deviation After
Fault
Machine angles
%&'
$#
'
'
$
$
angle in degrees
speed deviation in, pu
"
$
$
#
!
times(s)
!
times(s)
Figure 4 Using Conventional Lead-Lag Controller
Speed Deviation After Fault
times(s)
Figure 5
Untitled-58
Machine angles
angle in degrees
speed in, pu
61
times(s)
FLPSS- Using 7 Mixed-Gaussian/Triangular MF’s
02/16/2007, 18:07
62
M. F. OTHMAN, M. MAHFOUF & D. A. LINKENS
Speed Deviation After Fault
Machine angles
angle in degrees
speed in, pu
#
#
times(s)
Figure 6
times(s)
FLPSS- Using 7 Triangular MF’s with MOM defuzzification
Machine angles
Speed Deviation After Fault
$
$
angle in degrees
speed in, pu
+
#
$
times(s)
times(s)
Figure 7 FLPSS- Using 5 Gaussian MF’s
Machine angles
Speed Deviation After Fault
#
$
angle in degrees
speed in, pu
times(s)
times(s)
Figure 8 ANFIS - Using 3 MF’s
Untitled-58
62
02/16/2007, 18:07
DESIGNING POWER SYSTEM STABILIZER FOR MULTIMACHINE POWER SYSTEM
Machine
angles
%&'
Speed
Deviation After Fault
#
$
#
'
'
angle in degrees
speed in, pu
"
63
+
!
!
times(s)
times(s)
Figure 9 ANFIS- Using 5 MF’s
ACKNOWLEDGEMENTS
The first author acknowledges financial support for this study from UTM-SLAB,
Malaysia.
REFERENCE
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Untitled-58
Abido, M. A. (1999). ‘A novel Approach to conventional power system stabilizer design using tabu
search’, Int. Journal of Eec Power and Energy System. 21(6): 443–454.
Barreiros, JL, Silva A. S., A. J. Simoes Costa (1998) ‘A self-tuning generalized predictive power system
stabilizer’ Electric Power & Energy Systems. 20(3): 213–219.
PST. (1997) 'Power System Toolbox for Matlab’ Cherry Tree Scientific Software, Canada.
Hsu, K. Y., C. H. Cheng. (1990) ‘Design of Fuzzy Power System Stabilizer for multimachie power systems', IEE Pt C, May.
Hsu, Y. Y., C. R. Chen. (1991). ‘Tuning of Power System Stabilizer using Artificial Neural Network’
IEEE Trans. Energy Convers. 6(4): 616–619.
Kundur, P. (1994) Power System Stability and Control. Mc Graw-Hill Press.
Mathwork, Co (1999) Matlab V5.3.
63
02/16/2007, 18:07